Lawyers for Bank of America Corp. and the Justice Department met on Tuesday to continue negotiating a potential mortgage-securities settlement but remain far apart on the size and scope of the penalty, according to people familiar with the matter.

The bank is offering $13 billion, including cash and consumer relief, but the Justice Department wants a much heftier cash penalty, these people said. Another big sticking points is how the settlement would be structured, with Bank of America pushing for a bigger portion of the...